This paper compares the performance and characteristics of two innovative sodium-cooled fast reactors (iSFRs) with different fuel types. One is loaded only with low-enriched uranium fuel and the other one is loaded with spent nuclear fuels. The iSFR is designed based on the Korean prototype Gen-IV sodium-cooled fast reactor in order to enhance the safety and economics through innovative core designs. The iSFR core is also equipped with two new and unique passive safety devices called floating absorber for safety at transient and static absorber feedback equipment to improve the safety performance of iSFR and particularly to address the positive coolant void reactivity coefficients. In this work, several important parameters such as core reactivity, kinetics parameters, reactivity feedback coefficients, power profiles, and fuel composition changes have been analyzed by using the McCARD Monte Carlo code. The sub-channel code MATRA-LMR is used to perform the thermal-hydraulics analysis. The balance of reactivity method has also been utilized to investigate the self-controllability of the two iSFR cores.